Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 5

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych:  claw-free
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

2-factors in claw-free graphs

100%
Chen G., Faudree J., Gould R., Saito A.
Discussiones Mathematicae Graph Theory
|
2000
|
tom 20
|
nr 2
165-172
EN
We consider the question of the range of the number of cycles possible in a 2-factor of a 2-connected claw-free graph with sufficiently high minimum degree. (By claw-free we mean the graph has no induced $K_{1,3}$.) In particular, we show that for such a graph G of order n ≥ 51 with δ(G) ≥ (n-2)/3, G contains a 2-factor with exactly k cycles, for 1 ≤ k ≤ (n-24)/3. We also show that this result is sharp in the sense that if we lower δ(G), we cannot obtain the full range of values for k.
2
Content available remote

On the Numbers of Cut-Vertices and End-Blocks in 4-Regular Graphs

100%
Wang D., Shan E.
Discussiones Mathematicae Graph Theory
|
2014
|
tom 34
|
nr 1
127-136
EN
A cut-vertex in a graph G is a vertex whose removal increases the number of connected components of G. An end-block of G is a block with a single cut-vertex. In this paper we establish upper bounds on the numbers of end-blocks and cut-vertices in a 4-regular graph G and claw-free 4-regular graphs. We characterize the extremal graphs achieving these bounds.
3
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

On graphs G for which both g and G̅ are claw-free

100%
Fujita S.
Discussiones Mathematicae Graph Theory
|
2005
|
tom 25
|
nr 3
267-272
EN
Let G be a graph with |V(G)| ≥ 10. We prove that if both G and G̅ are claw-free, then min{Δ(G), Δ(G̅)} ≤ 2. As a generalization of this result in the case where |V(G)| is sufficiently large, we also prove that if both G and G̅ are $K_{1,t}$-free, then min{Δ(G),Δ(G̅)} ≤ r(t- 1,t)-1 where r(t-1,t) is the Ramsey number.
4
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Potential forbidden triples implying hamiltonicity: for sufficiently large graphs

100%
Faudree R., Gould R., Jacobson M.
Discussiones Mathematicae Graph Theory
|
2005
|
tom 25
|
nr 3
273-289
EN
In [1], Brousek characterizes all triples of connected graphs, G₁,G₂,G₃, with $G_i = K_{1,3}$ for some i = 1,2, or 3, such that all G₁G₂ G₃-free graphs contain a hamiltonian cycle. In [8], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G₁,G₂,G₃, none of which is a $K_{1,s}$, s ≥ 3 such that G₁G₂G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In [6], a characterization was given of all triples G₁,G₂,G₃ with none being $K_{1,3}$, such that all G₁G₂G₃-free graphs are hamiltonian. This result, together with the triples given by Brousek, completely characterize the forbidden triples G₁,G₂,G₃ such that all G₁G₂G₃-free graphs are hamiltonian. In this paper we consider the question of which triples (including $K_{1,s}$, s ≥ 3) of forbidden subgraphs potentially imply all sufficiently large graphs are hamiltonian. For s ≥ 4 we characterize these families.
5
Content available remote

Forbidden Pairs and (k,m)-Pancyclicity

88%
Crane C. B.
Discussiones Mathematicae Graph Theory
|
2017
|
tom 37
|
nr 3
649-663
EN
A graph G on n vertices is said to be (k, m)-pancyclic if every set of k vertices in G is contained in a cycle of length r for each r ∈ {m, m+1, . . . , n}. This property, which generalizes the notion of a vertex pancyclic graph, was defined by Faudree, Gould, Jacobson, and Lesniak in 2004. The notion of (k, m)-pancyclicity provides one way to measure the prevalence of cycles in a graph. We consider pairs of subgraphs that, when forbidden, guarantee hamiltonicity for 2-connected graphs on n ≥ 10 vertices. There are exactly ten such pairs. For each integer k ≥ 1 and each of eight such subgraph pairs {R, S}, we determine the smallest value m such that any 2-connected {R, S}-free graph on n ≥ 10 vertices is guaranteed to be (k,m)-pancyclic. Examples are provided that show the given values are best possible. Each such example we provide represents an infinite family of graphs.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.